2006_A New Algorithm for Distorted Fingerprints Matching Based on Normalized Fuzzy Similarity Measure

8/4/2019 2006_A New Algorithm for Distorted Fingerprints Matching Based on Normalized Fuzzy Similarity Measure

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768 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 15, NO. 3, MARCH 2006

line. Kovacs-Vajna et al. [17] also proposed a method based

on triangular matching to cope with the strong deformation

offingerprint images, demonstrating graphically that the large

cumulative effects can be a result from the small local distor-

tions. Bazen et al. [18] employed a thin-plate spline model

to describe the nonlinear distortions between the two sets of

possible matching minutiae pairs. By normalizing the inputfingerprint with respect to the template, this method is able to

perform a very tight minutiae matching.

Different from the above mentioned methods, we propose an

algorithm based on fuzzy theory to deal with the nonlinear dis-

tortion in fingerprint images. First, an algorithm was defined to

deal with the spurious minutiae. Then the algorithm aligns the

template and inputfingerprints using the registration method de-

scribedbyLuo etal.[19],andlocaltopologicalstructurematching

wasintroducedto improve the robustnessof global alignment.Fi-

nallya novel similaritycomputingmethod based on fuzzytheory,

NFSM,wasconductedtocomputethesimilaritybetweenthetem-

plateandinput fingerprints. Experimental results indicate thatthe

proposedalgorithmworkswellwiththenonlineardistortions.Fordeformed fingerprints, the algorithm gives considerably higher

matching scores compared to conventionalmatching methods. In

fingerprints database DB1 and DB3 of FVC2004, the distortion

between some fingerprints from the same finger is large, but our

algorithm performs well. The equal error rates (EER) are 4.37%

and 1.64% on DB1 and DB3, respectively.

This paper is organized as follows. Section II indicates out the

fingerprint feature representation and extraction. A method is

defined to deal with the spurious minutiae. Section III describes

the local topological structure matching. Section IV proposes

the novel method, NFSM, which is applied to compute the sim-

ilarity between the template and input fingerprints. The perfor-mance of the proposed algorithm is shown by experiments in

Section V. Section VI presents our conclusion and discussion.

II. FEATURE REPRESENTATION AND EXTRACTION

For an input fingerprint image, the method described by

Hong et al. [20] is used to enhance the image, and the thinned

ridge map is obtained. The thinned ridge map is postpro-

cessed by using Luos method [21]. Then the minutiae set

is detected by using Hongs method [20]. For each belongs

to , the associate ridges or valleys in are traced and some

sample points with constant intervals are recorded. The

minutiae set and the sample points on the associate ridges and

valleys provide information for both alignment and discrimina-

tion. An example of the feature set of a live-scan fingerprint is

provided in Fig. 1.

A critical and difficult step in fingerprint matching is to re-

liably extract minutiae from the input fingerprint images. The

performance of a minutiae extraction algorithm highly relies on

the quality of the input fingerprint images. In an idealfingerprint

image, ridges and valleys alternate and flow in a local constant

direction and minutiae are anomalies of ridges, i.e., ridge end-

ings and ridge bifurcations. In such situations, the ridges can be

easily detected and minutiae can be precisely located from the

thinned ridges. However, in reality, approximately 10% [20] ofacquired fingerprint images are of poor quality due to variations

Fig. 1. Feature set of a live-scan fingerprint image. (a) Original fingerprintimage. (b) Thinned ridge image with minutiae and sample points of (a).

in impression conditions, ridge configuration, skin conditions,

acquisition devices, and noncooperative attitude of subjects, etc.

The ridge structuresin poor-qualityfingerprintimages arenot al-

ways well-defined and, therefore, cannot be correctly detected.

A significant number of spurious minutiae may be created as aresult. In order to ensure that the performance of the minutiae

extraction algorithm will be robust with respect to the quality of

input fingerprint images, an enhancement algorithm which can

improve the clarity of the ridge structures is necessary. However,

forpoorfingerprint image, somespuriousminutiae may stillexist

afterfingerprint enhancement and postprocessing.It is necessary

to propose a method to deal with the spurious minutiae.

A method to judge whether an extracted minutia is a true one

has been proposed in this paper. According to our work, the dis-

tance between true minutiae is generally greater than threshold

(thre). While near the spurious minutiae, there are usually other

spurious minutiae. On the other hand, spurious minutiae are usu-

ally detected at the border of fingerprint image. Examples of

spurious minutiae in poor quality fingerprint images are shown

in Fig. 2.

The following algorithm is performed to detect the spurious

minutiae. In this process, a few true minutiae may be considered

as spurious ones, but this does not affect further match process.

Step 1: Judge whether the minutia is close

to the border of the fingerprint image.

The fingerprint mask is obtained by using

Hongs algorithm [20]. The distance disMB

between the minutiae and the fingerprint

border is computed. If (ac-

cording to our work, ), then it is

considered as spurious minutia, else goto

step 2.

Step 2: Search minutiae center around the

minutia Mi within thre radius, obtain the

number of minutiae num.

Step 3: If (according to our

work, ), then it is considered as

spurious minutia, otherwise as a true one.

It is an efficient and simple method to detect the spurious

minutiae. None of the detected spurious minutiae are partici-pated in the further match process.


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CHEN et al.: NEW ALGORITHM FOR DISTORTED FINGERPRINTS MATCHING 769

Fig. 2. Examples of spurious minutiae in poor quality fingerprint images. Theimageshave been cropped and scaledfor view. (a) Original image.(b) Enhancedimage of (a), (c) original image, (d) enhanced image of (c). Many spuriousminutiae were detected in the process of minutiae extraction. Near the spuriousminutiae, there are usually other spurious minutiae as indicated in ellipses, andspurious minutiae are usually detected at the border of fingerprint image asshown in rectangles.

III. MATCHING USING LOCAL TOPOLOGICAL STRUCTURE

The proposed matching algorithm has two steps. First, Luos

matchingmethod[19]whichmodifiedfromJainetal.salgorithm[22] has been used to process the coarse match. A changeable

bounding box is applied during the matching process which

makes it more robust to nonlinear deformations between the

fingerprint images. Fig. 3 shows the illustrative diagram for

changeable sized bounding box. The value of angle_size and

radius_size of the bounding box in every minutia is changed

according to the radius of the minutia. If the radius of the

template minutia is larger, then its bounding box will have a

larger radius_size and a smaller angle_size. We suppose an

approximate alignment has already beenestablished at thisstage.

If the approximate alignment is wrong, the further matching

steps cannot recover this error. Then, local topological structure

match is introduced to improve the robustness of match.

A. Defining of Local Topological Structure

Let denote a minutia in the fingerprint image and

are the minutiae circled around within

radius. Feature vector is used to describe

the relationship between and denotes the distance

between and denotes the angle between the orien-

tation of minutia and the direction from to

denotes the angle between the orientation of minutia

and the direction from to . It is easy to see that the local

topological structure feature vector isindependent from the rotation and translation of the fingerprint.

Fig. 3. Illustrative diagram for changeable sized bounding box.

Fig. 4. Local topological structure of P .

Fig. 4 shows the meaning of each parameter. The local topo-

logical structure of is defined as the following:

B. Local Topological Structure Matching

Suppose is a minutia in the template fingerprint,

are minutiae circled around within radius.

Then, the local topological structure of can be obtained as

Suppose is a minutia in the input fingerprint and the input

fingerprint is deformed. For the deformed input fingerprint,

minutiae are searched in a circle around within

radius. is the distance tolerance. Suppose are

minutiae circled around within radius. Then, the local

topological structure of can be expressed as

The following algorithm is used to determine whether twominu-

tiae and are matched.

Step 1: For and , matched each

entry , in the local topological struc-ture and each entry , in


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Fig. 5. Illustrative diagram for matching P Q ( l e n ; ; ) , andR S ( l e n ; ; )

. (a) Topological structure ofP Q

andR S

.

(b) The adaptive matching bounding box.

the local topological structure , obtained the matched

number of and .

Three parameters , , are calculated as the

following:

(1)

(2)

(3)

An adaptive matching bounding box is

used to determine whether and is matched. The size

of matching box changes according to the distance as

seen in (4) and (5), shown at the bottom of the page, where

, . The purpose for using a change-

able sized bounding box is to deal with nonlinear deformation

more robustly. Fig. 5 shows the illustrative diagram for matching

, and .

When the distance of is small, a small deformation will

mean a large change of the radial angle while the change ofradius remains small. In this case the of the bounding box

should be larger and the of the bounding box should be

smaller. On the other hand, when the distance of is large,

a small change in radial angle will cause a large change in the

position of the minutia. The radius can have larger deformation

as the accumulation of deformation from all the regions between

and [17]. In this case, the of the bounding box

should be larger and the should be smaller.

If (1)(3) satisfy the following conditions:

(6)

(7)

(8)

then and are considered as matched.

Step 2: If then goto Step 3, else and

are considered as not matched.

Fig. 6. Two cases of the local topological structure of P and R satisfy therequirement of step2. (a) Minutia

P

is actually not matched with minutiaR

.(b) Minutia

P

is matched with minutiaR

.

Step 3: Fig. 6 shows two cases that the local topological

structure of and satisfy the requirement of step2. In case

(a), there are three minutiae , , circled around

within radius and radius, but there are six minutiae

circled around with radius. Although

, minutia is actually not matched with

minutia . In case (b), there are three minutiae , , cir-

cled around within radius but six minutiae

circled around within radius, and there are sixminutiae circled around with radius.

As the fingerprint is deformed, minutia is considered as

matched with minutia .

Therefore, we need to handle the above two cases. We ob-

tained another two local topological structure of

and . is obtained by searching

minutiae circled around within radius. Suppose these minu-

tiae are . Then the local topological structure of

can be expressed as

is obtained by searching minutiae circled

around within radius. Suppose these minutiae

are . Then, the local topolog-

ical structure of can be expressed as

Then, using the algorithm described in step 1), match the local

topological structure and , obtain the

matched number .

Step 4: If , then is matched with ,

else not matched.

Experiments were performed to evaluate the contribution of

the proposed local topological structure match algorithm on

if

if

otherwise(4)

if

ifotherwise. (5)


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TABLE ICOMPARISON OF THE ALGORITHM WITH AND WITHOUT THE PROPOSED

LOCAL TOPOLOGICAL STRUCTURE MATCH ON FVC2002 DB

FVC2002 DB. Table I illustrates the comparison of the algo-

rithm with and without the proposed local topological structure

match on FVC2002 DB. It is clear that the proposed local

topological structure match algorithm has obviously improved

the overall performance.

IV. NORMALIZED FUZZY SIMILARITY MEASURE

Computing the similarity between deformed template and

input fingerprints is a difficult task. In some algorithms [3], [18],

the number of matching minutiae was only used to compute

the similarity between template and input fingerprints. Most

algorithms increase the size of the bounding boxes in order to

tolerate the further apart of matched minutiae pairs because ofplastic distortions and, therefore, to decrease the false rejection

rate (FRR). However, as a side effect, this method may lead

higher false acceptance rate (FAR) by making nonmatching

minutiae get paired. Different from the above mentioned algo-

rithm, we proposed a novel similarity computing method based

on fuzzy theory to calculate the similarity between template

and input fingerprints images.

A. Feature Representation of Similarity Measure

Two features are selected: the number of matched sample

points (n) and the mean distance difference of the matched minu-

tiae pairs (d) in the process of similarity computing . Using the

proposed algorithm defined in Section III, the matched minutiae

pairs between template and input fingerprints can be obtained.

The corresponding sample points are considered to match if

their associated minutiae are matched. If the number of sample

points for one minutia in a pair is different from the second

minutia of the pair, we set the smaller number as the number of

matched sample points. Suppose there are matched minutiae

pairs, and there are matched sample points for every minutiae

pair, then the sum of matched sample points is calculated as

follows:

(9)

Fig. 7. Probability distribution ofn

in Genuine match and Imposter match onFVC2002 DB1.

Fig. 8. Probability distribution ofd

in Genuine match and Imposter match onFVC2002 DB1.

and the mean of distance difference between every two minutiae

is calculated as follows:

(10)

Where the meaning of can be seen in expression (1).

Experiments were performed to characterize the features:

and . The experiments were done on FVC2002 DB1. It con-

tains 800 fingerprint images captured by optical sensor Identix

TouchView II. According to FVC rules [1], each sample ismatched against the remaining samples of the same finger in

genuine match. Hence, the total number of genuine tests (in case

no enrollment rejections occur) is: .

In imposter match, the first sample of each finger is matched

against thefirst sample of the remainingfingers. Hence, the total

number of false acceptance tests (in case no enrollment rejec-

tions occur) is: . All of n and d samples

from genuine match and imposter match were used to construct

fuzzy feature sets and , respectively. Figs. 7 and 8 show

the probability distribution of n and d in genuine match and im-

poster match on FVC2002 DB1. From Figs. 7 and 8, wefind that

has excellent classification performance and the classification

performance of d is also good. Fig. 9 shows a scatter plot of dagainst n for all examples in genuine match and imposter match


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Fig. 9. Scatter plot of d against n for all examples on FVC2002 DB1.

on FVC2002 DB1. The fuzzy feature sets and are clus-

tered into two classes. One is corresponding to genuine match

samples and the other is to imposter match samples.

B. NFSM Measure

Fuzzy features were used to represent and . Each character

is associated with a fuzzy feature that assigns a value (between

0 and 1) to each feature vector in the feature space. The value,

named degree of membership, illustrates the degree of similarity

of the template and input fingerprints.

A fuzzy feature on the feature space is defined by a

mapping named as the membership function.

For any feature vector , the value of is called the

degree of membership of to the fuzzy feature . The value ofis more close to 1, the input fingerprint is more similar

to the template one. For the fuzzy feature , there is a smooth

transition for the degree of membership to besides the hard

cases and . It is clear

that a fuzzy feature degenerates to a conventional feature set if

the range of is instead of .

Building or choosing a proper membership function is an ap-

plication dependent issue. Some most commonly used prototype

membership functions are cone, exponential, and Cauchy func-

tions [23]. In the proposed algorithm, the Cauchy function is

chosen due to its good expressiveness and high-computational

efficiency [24].

The Cauchy function: , is defined as

(11)

where , and , , . is the center

location of the fuzzy set, represents the width ( for

) of the function, and determines the smoothness

of the function. Generally, and portray the grade of fuzzi-

ness of the corresponding fuzzy feature. For fixed , the grade

of fuzziness increases as decreases. For fixed , the grade offuzziness increases as increases.

Accordingly, feature is represented by fuzzy feature

whose membership function, , is defined as

(12)

where represents the distance between

and and are the genuine and imposter match clusters

center of fuzzy set .

Feature is represented by fuzzy feature whose member-

ship function, , is defined as

(13)

where represents the distance between

and and are the genuine and imposter match clusters

center of fuzzy set .An intrinsic property of membership function (12) and

(13) is that the farther a feature vector moves away from the

cluster center, the lower the degree of membership is to the

fuzzy feature. At the same time, the degrees of membership

to the other fuzzy features may be increasing. This clearly

describes the gradual transition of two clusters. Table II shows

the respective classification performance of and

on FVC2002 DB.

In order to achieve the better classification performance,

and are combined. The detailed analysis on

combining classifiers can be seen in the literatures [25][27].

After combination, the similarity is needed to normalize to

. Four rules were used to combine and . In

these four rules, the similarity is always in the real interval

because and are always within .

1) Max rule:

(14)

2) Min rule:

(15)

3) Product rule:

(16)

4) Mean rule:

(17)

Experiments were performed to evaluate four similarity com-

puting rules on FVC2002 DB. Table II shows the comparison

of performance on FVC2002 DB in different similarity com-

puting rules. On DB1, if only is used to classify in fin-

gerprint matching, EER is 3.03%, and if only is used to

classify in fingerprint matching, EER is 20.13%. While using

the product rule to compute the similarity, EER is decreased to0.19%. From Table II, we can clearly tell that the performance


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TABLE IICOMPARISON OF PERFORMANCE ON FVC2002 DB

IN DIFFERENT SIMILARITY COMPUTING RULES

Fig. 10. Experimental results of the proposed algorithm on FVC2002 DB1.

of product rule is the best while the performance of max rule is

the worst. Hence, the product rule was selected in the proposed

algorithm to compute the similarity between the template and

input fingerprints. Fig. 10 shows the experimental results of the

proposed algorithm on FVC2002 DB1.

V. EXPERIMENTAL RESULTS

The proposed algorithm has been participated in

FVC2004. In FVC2004, databases are more difficult than in

FVC2000/FVC2002 ones. In FVC2004, the organizers have

particularly insisted on: distortion, dry, and wet fingerprints.

Especially in fingerprints database DB1 and DB3 of FVC2004,the distortion between some fingerprints from the same finger is

Fig. 11. Example of large distortion from FVC2004 DB1. (a) 102_3.tif;(b) 102_5.tif; (c) image which (a) (after registration) was added to (b). In therectangle region, the corresponding minutiae are approximately overlapped.While in the ellipse region, the maximal vertical difference of correspondingminutiae is above 100 pixels.

large. Our work is to solve the problem of distorted fingerprintmatching, so the evaluation of the proposed algorithm is

mainly focused on DB1 and DB3 of FVC2004. The proposed

algorithm is also compared with the one described by Luo et

al. [19] and the one proposed by Bazen et al. [18].

A. Performance On FVC2004 DB1

The fingerprints of FVC2004 DB1 were acquired through

CrossMatch V300 (Optical sensor). The size of the image is

640 480 pixels with the resolution about 500 dpi. The fin-

gerprint database set A contains 800 fingerprint images cap-

tured from 100 different fingers, eight images for each finger.

Fig. 11 shows an example of large distortion from FVC2004DB1 (102_3.tif and 102_5.tif). While the corresponding minu-

tiae in green region are approximately overlapped, the maximal

vertical difference of corresponding minutiae in red region is

above 100 pixels. Fig. 12 indicates our enhanced and matched

results on 102_3.tif and 102_5.tif. Using the proposed algo-

rithm, the similarity between these twofingerprints is 0.420 082.

Fig. 13 presents another fingerprint pair with large distortion

from FVC2004 DB1. The similarity between these two finger-

prints is 0.650 000. The performance of the proposed algorithm

on FVC2004 DB1 is shown in Fig. 14, and from which we find

that the similarity threshold at EER point is about 0.28, so we

judge that the above two fingerprint pairs come from the same

finger. The two matches are successful. The EER of the pro-posed algorithm on FVC2004 DB1 is about 4.37%. The average

time for matching two minutiae sets is about 0.77 s on PC AMD

Athlon (1.41 GHz).

B. Performance On FVC2004 DB3

The fingerprints of FVC2004 DB3 were acquired through

thermal sweeping sensor FingerChip FCD4B14CB by Atmel.

The size of the image is 300 480 pixels with the resolution

of 512 dpi. In this fingerprints database, the distortion between

some fingerprints from the same finger is large. Fig. 15 shows a

fingerprint pair with large distortion from FVC2004 DB3. Using

the proposed algorithm, the similarity between these twofinger-prints is 0.484 111. The performance of the proposed algorithm


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Fig. 12. Experimental results of the proposed algorithm on 102_3.tif and

102_5.tif in FVC2004 DB1. The images have been cropped and scaled forview. (a) 102_3.tif. (b) Enhanced image of 102_3. (c)102_5.tif. (d) Enhancedimage of 102_5. The similarity of these two fingerprints is 0.420 082.

Fig. 13. Experimental results of the proposed algorithm on 109_3.tif and

109_4.tif in FVC2004 DB1. The images have been cropped and scaled forview. (a) 109_3.tif. (b) Enhanced image of 109_3. (c) 109_4.tif. (d) Enhancedimage of 109_4. The similarity of these two fingerprints is 0.650 000.

on FVC2004 DB3 is shown in Fig. 16. It indicates that the sim-

ilarity threshold at EER point is about 0.26, so we can judge

that the fingerprint pair comes from the same finger. The EER

of our algorithm on FVC2004 DB3 is about 1.64%. The average

time for matching two minutiae sets is about 0.81 s on PC AMDAthlon (1.41 GHz).

Fig. 14. Experimental results of the proposed algorithm on FVC2004DB1_A.The fingerprint images were acquired through optical sensor.

Fig. 15. Experimental results of the proposed algorithm on 103_2.tifand 103_4.tif in FVC2004 DB3. The images have been scaled for view.(a) 103_2.tif. (b) Enhanced image of 103_2. (c) 103_4.tif. (d) Enhanced imageof 103_4. The similarity of these two fingerprints is 0.484 111.

Fig. 16. Experimental results of the proposed algorithm on FVC2004DB3_A.The fingerprint images were acquired through thermal sweeping sensor.

The proposed algorithm has good performance on finger-

prints database DB2 and DB4 of FVC2004 as well. EER are

2.59% and 0.61%, respectively. The processing time is 0.58and 0.56 s, respectively.


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TABLE IIICOMPARISON OF MATCHING SCORE IN THE NFSM

ALGORITHM TO LUOS METHOD

Fig. 17. Example of false acceptance on a pair of fingerprints capturedfrom CrossMatch sensor. The images have been cropped and scaled for view.(a) Original image. (b) Enhanced image of (a). (c) Original image. (d) Enhanced

image of (c). The fingerprint pair is very similar, but they are from differentfinger. The similarity of the two fingerprints is 0.431 516.

C. Comparison of NFSM With Other Algorithm

The proposed algorithm is compared with the one described

by Luo et al. [19]. The Comparison is performed on FVC2004

DB1. In Luos method, a changeable bounding box was used

during the matching process. It is more robust to nonlinear de-

formations between the fingerprint images. However, the dis-

tortion among some fingerprints from the same finger captured

from the CrossMatch sensor is too large. In order to tolerate

matching minutiae pairs that are further apart because of distor-

tions, the size of the bounding boxes has to be increased. How-

ever, as a side effect, it gives a higher probability for those non-

matching minutiae pairs to get paired, resulting in a higher falseacceptance rate. Table III lists the comparison of matching score

of the proposed algorithm to Luos method. It is clear that case

1 and case 2 have been successfully matched in our NFSM al-

gorithm. While for Luos method, when size of the bounding

boxes is 15, case 1 and case 2 are false rejected, and when size

of the bounding boxes is increased to 25, case 2 is accepted but

case 1 is false rejected, meanwhile EER is increased from 9.13%

to 9.92%. Moreover, EER of the proposed algorithm is 4.37%,which is much lower than Luos method of 9.13%.

The proposed algorithm is also compared with Bazens

method [18]. In their training database of FVC2002 DB1, for

Bazens algorithm, the EER of the ROC turned out to be 1.8%

with for elastic matching. While in our algorithm, the

EER on FVC2002 DB1 is only about 0.19%. The experimental

results of our algorithm on FVC2002 DB1 are shown in Fig. 10.

The results conform that the performance of the proposed algo-

rithm surpasses Bazens algorithm.

VI. CONCLUSION AND DISCUSSION

Coping with nonlinear distortions in the matching algorithmis a challenging task. In this paper, we proposed a novel algo-

rithm to deal with the nonlinear distortion in fingerprint images.

A novel similarity computing method based on fuzzy theory,

NFSM, is introduced to compute the similarity between the tem-

plate and input fingerprints. Experimental results show that the

algorithm gives considerably higher matching scores compared

to conventional matching algorithms for deformed fingerprints.

Our algorithm has been participated in FVC2004. The Partici-

pant ID is P071 (open). The detailed performance of the pro-

posed algorithm on FVC2004 can be seen from the website

http://bias.csr.unibo.it/fvc2004/default.asp. In fingerprints data-

base DB1 and DB3 of FVC2004, the distortion between some

fingerprints from the same finger is large. However, EER areonly 4.37% and 1.64% on DB1 and DB3, respectively, in our

algorithm, and it performs well on processing time, the average

time for matching two minutiae sets is about 0.67 s.

However, there are still few false acceptances in fingerprint

matching process. Fig. 17 shows an example of false acceptance

on a pair offingerprints captured from CrossMatch sensor. The

pair is very similar, but they are from different finger. Further

investigation is going on to advance the algorithm for its false

acceptance which occasionally happens.

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Xinjian Chen received theB.S. degreein geophysicsfrom Centre South University of Technology, China,in 2001. He is currently pursuing the Ph.D. degreeat the Institute of Automation, Chinese Academy ofSciences, Beijing.

His research interests include pattern recognition,machine learning, image processing, and their appli-cations in biometrics.

Jie Tian (SM02) received the Ph.D. degree (with

honors) in artificial intelligence from the Institute ofAutomation, Chinese Academy of Sciences, Beijing,in 1992.

From 1994 to 1996, he was a Postdoctoral Fellow

with the medical image processing group, Universityof Pennsylvania, Philadelphia. Since 1997, he hasbeen a Professor with the Institute of Automation,Chinese Academy of Sciences. His research interestsinclude pattern recognition, machine learning, imageprocessing and their applications in biometrics, etc.

Xin Yang received the Ph.D. degree in precision in-struments from TianJing University, China, in 2000.

She is a Postdoctoral Fellow with Institute ofAutomation, Chinese Academy of Sciences, Beijing.Her research interests include pattern recognition

and its applications in biometrics.

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